The Russell group of leading research universities has rejected claims that its members are failing their students from disadvantaged backgrounds because they do little to improve their post-graduation employment prospects.

The research, published by the thinktank CentreForum, argues government policy is too narrowly focused on encouraging universities to recruit more students from disadvantaged backgrounds, rather than on what happens to those students during and after their studies.

It proposes that a "social mobility graduate index" be used to measure how successful universities are at finding employment for all of their students, with greater weight given to students from areas with very low rates of higher education.

A prototype of the index put University College London's School of Pharmacy in first place, followed by the University of St Mark & St John – nicknamed Marjon – in Plymouth. Other than the School of Pharmacy, not a single Russell group university appeared in the top 20 and only Aston University represented the pre-1992 universities.

Professor Michael Brown, a former vice-chancellor of Liverpool John Moores University and the author of the report, said: "In terms of graduation performance and employment outcomes, students from areas of high disadvantage have a lower success rate than those from more advantaged backgrounds.

"And despite the political focus on access to Russell group universities, the most selective institutions do not necessarily deliver the best professional graduate outcomes for disadvantaged students either. It is time to raise the game."

But Wendy Piatt, director general of the Russell group, said: "We reject the findings and methodology of this report. It makes very strange assumptions about social mobility.

"It fails, too, to recognise that those students from more disadvantaged backgrounds are more likely to complete their degree at a Russell group university than they are at other institutions."

Piatt said the index used only a survey of graduate employment six months after completion of studies and gave a lower weight to students undertaking postgraduate study.

"In fact, graduates from Russell group universities go on to earn more than other graduates, are more likely to be in high-skilled jobs and earn 24% more per hour than their peers from other universities," Piatt said.

"Employers know the quality of students from our universities is high: that is why nine out of the top 10 universities most often targeted by Britain's top graduate employers are Russell group universities."

Brown said the point was not to criticise Russell group members so much as demonstrate that many less-selective universities were doing a better job of helping graduates into professional employment.

The report says that Russell group universities do badly in the social mobility index because so few of their students come from deprived backgrounds. While 70% of Russell group undergraduates are in the two most advantaged quintiles as measured by participation in higher education, only 5% were from the lowest participation areas.